Linear Algebra with Applications (3rd Edition)

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110.201 Linear Algebra1st Quiz SolutionFebruary 15, 2005Problem 1Given the following system of equations:3x+ 2y-5z= 14x-y+z= 0x-z= 2find all solutions using Gauss-Jordan elimination procedure. Is this an exampleof consistent system? Why?Solution:We use Gauss-Jordan:32-54-1110-1102We rewrite the matrix as :10-132-54-11210-3×(I)-4×(I)then:10-102-20-152-5-8÷2then:1
10-101-10-152-52-8+(II)then:10-101-10042-52-212÷4then:10-101-10012-52-218+(III)+(III)then we have:100010001-58-418-218Therefore, we have the answer :x=-58y=-418z=-218Problem 2Find the rank of the following matrix-138-21-139-131-3-91-300002Solution:We find reduced row-echelon form of this matrix:-138-21-139-131-3-91-300002×(-1)+(II)÷22
then:1-3-82-1-139-130000000001+(I)then:1-3-8

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